cancels common poles and zeros in the TransferFunctionModel tfm.
cancels only common pole-zero pairs ei for which crit[ei] is True.
Details and Options
- The poles and zeros are computed using TransferFunctionPoles and TransferFunctionZeros.
- TransferFunctionCancel accepts the option Tolerance.
- With the setting Tolerance->ϵ, poles and zeros with will be canceled.
Examplesopen allclose all
Basic Examples (3)
Cancel the common pole-zero pair at the origin:
Cancel common pole-zero pairs of a fourth-order system:
The common pole-zero pair is evident by factoring the transfer function:
Cancel pole-zero pairs for a discrete-time system:
Cancel pole-zero pairs for a system with input delay:
Cancel common pole-zero pairs that are stable:
Cancel pole-zero pairs with tolerance not greater than 0.01:
With zero tolerance nothing is canceled:
This system has two pole-zero pairs whose tolerance is less than or equal to 0.6:
Cancel the pair with frequency greater than 9 radians per time unit:
Visualize the responses of the three systems to a unit step input:
Use TransferFunctionCancel to obtain a simpler representation of a highly oscillatory system in a series with a notch filter:
A system of higher order is obtained without the cancellation:
In most cases the pole-zero cancellation has a negligible effect on the overall dynamics:
Properties & Relations (1)
TransferFunctionCancel is equivalent to MinimalStateSpaceModel for SISO systems:
Possible Issues (2)
A system with an unstable pole-zero cancellation may appear stable:
But it is internally unstable:
TransferFunctionCancel does not support internal delays:
Wolfram Research (2010), TransferFunctionCancel, Wolfram Language function, https://reference.wolfram.com/language/ref/TransferFunctionCancel.html.
Wolfram Language. 2010. "TransferFunctionCancel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TransferFunctionCancel.html.
Wolfram Language. (2010). TransferFunctionCancel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TransferFunctionCancel.html